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Re: Simplifying expressions, and Alpha
*To*: mathgroup at smc.vnet.net
*Subject*: [mg31352] Re: [mg31336] Simplifying expressions, and Alpha
*From*: BobHanlon at aol.com
*Date*: Tue, 30 Oct 2001 04:35:36 -0500 (EST)
*Sender*: owner-wri-mathgroup at wolfram.com
In a message dated 2001/10/29 2:53:24 AM, msdawy at hotmail.com writes:
>i have 2 problems... i'd be very grateful if anyone could help me..
>1. some expressions return very complex expressions (e.g. when u solve
>a third degree equation), you get a very complex formula for the
>result. i am looking for a way to output the result in a
>human-readable format (like 2.3342218) not with many roots, and stuff
>like this, how can i do it?
>
>2. how can i find the point on a chi squared distribution where the
>CDF will be 0.995?
>
1. Use N[Solve[]], Solve[]//N, or just NSolve[].
2. The inverse of CDF is Quantile.
Needs["Statistics`ContinuousDistributions`"];
Quantile[ChiSquareDistribution[n], x]
2*InverseGammaRegularized[n/2, 0, x]
Quantile[ChiSquareDistribution[3], 0.995]
12.838156466598651
or using Solve
Solve[CDF[ChiSquareDistribution[n], q] == x, q]
{{q -> 2*InverseGammaRegularized[
n/2, 0, x]}}
Solve[CDF[ChiSquareDistribution[3], q] == 0.995, q]
{{q -> 12.838156466598651}}
Plot[Evaluate[Table[
CDF[ChiSquareDistribution[n], x],
{n, 1, 5, 2}]], {x, 0, 20},
PlotStyle -> Table[Hue[k/3], {k, 0, 2}],
AspectRatio -> 1];
Plot[Evaluate[Table[
Quantile[ChiSquareDistribution[n], x],
{n, 1, 5, 2}]], {x, 0, 1},
PlotStyle -> Table[Hue[k/3], {k, 0, 2}],
PlotRange -> {0, 20.5}, AspectRatio -> 1];
Bob Hanlon
Chantilly, VA USA
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